# Semi-major axis vs. apogee and perigee of orbit

This article on Wikipedia about Sedna states that its aphelion is 937 AU, its perihelion is 76 AU and its semi-major axis is 484 AU.

I would have expected the SMA to be half of the sum of the aphelion and perihelion. Is the article in error, or is there a difference that I'm not aware of?

I know apoapsis and periapsis are sometimes given relative the surface of the object being orbited, see this thread, but the effect should be negligible in this case and would anyway work in the opposite direction. Anything else I'm not seeing?

• I think this is just wikipedia being wikipedian and using a mix of sources. The linked Horizons page web.archive.org/web/20121119041320/http://home.surewest.net/… gives a = 503.5 pr=76 and ar=931, which are consistent Commented Dec 28, 2020 at 13:02
• What James said. And maybe someone misread a hand-written 931 as 937. Commented Dec 28, 2020 at 13:58

That's Wikipedia for you. The linked page demonstrates that Wikipedia is not a reliable source. Here are some of the problems:

• The values for aphelion, perihelion, semi-major axis, and eccentricity are inconsistent with one other.
• The values for perihelion, semi-major axis, and eccentricity are unsourced.
• The values for perihelion, semi-major axis, and eccentricity have far too much precision. Sedna was discovered 17 years ago, corresponding to about 0.15% of Sedna's orbital period. That's far too short of an arc length to justify five or six places of accuracy.
• The value for semi-major axis is inconsistent with other sources.
• The value for aphelion is poorly conducted original research. Footnote 5 (the reference for the aphelion value) states that the source is from osculating orbital elements about the solar system barycenter as retrieved from JPL Horizons. There are two key things wrong with this. One is the use of osculating elements, which can be deceiving. The other is using orbital elements about the solar system barycenter rather than about the Sun. This is just wrong.
• Barycentric elements for ETNOs are a thing; see Becker et al. 2018 table 3. Commented Dec 31, 2020 at 10:57

The Wikipedia article version in question took the aphelion and period from barycentric elements generated by JPL HORIZONS, and everything else from heliocentric elements listed in the JPL Small Body Database. Such mixing is inappropriate; as you noticed, it violates such rules as $$\frac{q}{1 - e} = \frac{Q}{1 + e} = a$$

Then what set of elements should be used? Different reputable sources give different answers:

Source epoch (JD) a (au) e q (au) Q (au) period (yr)
JPL SBDB 2459000.5 485 0.8426 76.26 893 10700
ESA AstDyS 2459200.5 492 0.8448 76.30 907 10900

Each of these agrees with JPL HORIZONS generated heliocentric elements at the same epoch:
(a=A, e=EC, q=QR, Q=AD, period=PR/365.25)

2459000.500000000 = A.D. 2020-May-31 00:00:00.0000 TDB
EC= 8.426174173255342E-01 QR= 7.625935860006692E+01 IN= 1.193068539938317E+01
OM= 1.442476602118453E+02 W = 3.113484332854660E+02 Tp=  2479370.363763529807
N = 9.240582598736822E-05 MA= 3.581177059136809E+02 TA= 3.218455376566813E+02
A = 4.845476373824915E+02 AD= 8.928359161649162E+02 PR= 3.895858255184166E+06
2459200.500000000 = A.D. 2020-Dec-17 00:00:00.0000 TDB
EC= 8.447267182563530E-01 QR= 7.630461951406060E+01 IN= 1.193098395982830E+01
OM= 1.442229068967588E+02 W = 3.112368043377307E+02 Tp=  2479295.935655418318
N = 9.047381952318225E-05 MA= 3.581818891812720E+02 TA= 3.223092404343984E+02
A = 4.914214387510542E+02 AD= 9.065382579880477E+02 PR= 3.979051640543999E+06


The Wikipedia article editors, citing the example of Kaib et al. 2009 for 2006 SQ372, prefer the smaller fluctuations of barycentric elements for long-period objects. JPL HORIZONS generates these:

2459000.500000000 = A.D. 2020-May-31 00:00:00.0000 TDB
EC= 8.495511413376979E-01 QR= 7.619102866448806E+01 IN= 1.192852412826112E+01
OM= 1.444015111060359E+02 W = 3.112855109740004E+02 Tp=  2479348.034461207222
N = 8.654118662895153E-05 MA= 3.582391002227536E+02 TA= 3.217633777437514E+02
A = 5.064247701307355E+02 AD= 9.366585115969829E+02 PR= 4.159869005997260E+06
2459200.500000000 = A.D. 2020-Dec-17 00:00:00.0000 TDB
EC= 8.495511411598982E-01 QR= 7.619102949417497E+01 IN= 1.192852416491278E+01
OM= 1.444015079430050E+02 W = 3.112855120822691E+02 Tp=  2479348.033582778648
N = 8.654118536876835E-05 MA= 3.582564085614893E+02 TA= 3.220917580263758E+02
A = 5.064247750469919E+02 AD= 9.366585205998089E+02 PR= 4.159869066571852E+06


In the same tabular format as above:

Source epoch (JD) a (au) e q (au) Q (au) period (yr)
HORIZONS barycentric 2459000.5 506 0.8496 76.19 937 11400

If you want to plot Sedna's position in planetarium software, you should use heliocentric elements because that's what the software expects.